How do you animate or otherwise envelope the noise of an animation?
To open the Graph Editor right panel, press N.

It looks like you can’t keyframe the F-curve modifiers values (I don’t know why though), but you can influence the course of the modifiers through the time by several methods:


As explained here: "You can create empty, set Noise on it, and copy location from it using constraint. So you can animate constraint’s influence, this is the way to key noise’s influence." Maybe it can suit your needs?
You can also open the Restrict Frame Range menu of your Noise modifier and play with its start and end values.
You can add an Envelope modifier after your Noise, add as many Control Points as you want and play with them to restrict or expand the effect of the Noise.